$s^2 + 2 = 0\\

s = \pm i\sqrt{2}\\

y_h(x) = c_0 \cos(\sqrt{2}x) + c_1 \sin(\sqrt{2}x)

$

$y_p(x) = c_2 e^x\\

c_2e^x + 2c_2 e^x = 3e^x\\

c_2 = 1\\

y_p(x) = e^x\\

y(x) = y_h(x) + y_p(x) = c_0 \cos(\sqrt{2}x) + c_1 \sin(\sqrt{2}x) + e^x

$

This is a linear diff eq. It just has a driving function.